754. Reach a Number

You are standing at position 0 on an infinite number line. There is a goal at position target.

On each move, you can either go left or right. During the n-th move (starting from 1), you take n steps.

Return the minimum number of steps required to reach the destination.

Example 1:

Input: target = 3
Output: 2
Explanation:
On the first move we step from 0 to 1.
On the second step we step from 1 to 3.

Example 2:

Input: target = 2
Output: 3
Explanation:
On the first move we step from 0 to 1.
On the second move we step  from 1 to -1.
On the third move we step from -1 to 2.

Note:

  • target will be a non-zero integer in the range [-10^9, 10^9].
  • Rust Solution

    struct Solution;
    
    impl Solution {
        fn reach_number(target: i32) -> i32 {
            let target = target.abs();
            let n = (((2 * target as i64) as f64 + 0.25).sqrt() - 0.5).ceil() as i32;
            let sum = n * (n + 1) / 2;
            if sum == target {
                n
            } else {
                let diff = sum - target;
                if diff % 2 == 0 {
                    n
                } else {
                    if n % 2 == 0 {
                        n + 1
                    } else {
                        n + 2
                    }
                }
            }
        }
    }
    
    #[test]
    fn test() {
        assert_eq!(Solution::reach_number(3), 2);
        assert_eq!(Solution::reach_number(2), 3);
        assert_eq!(Solution::reach_number(5), 5);
    }
    

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